Apwm2BpwmRC {lmomco} | R Documentation

## Conversion between A- and B-Type Probability-Weighted Moments for Right-Tail Censoring of An Appropriate Distribution

### Description

This function converts “A”-type Probability-Weighted Moments (PWMs, β^A_r) to the “B”-type β^B_r. The β^A_r are the ordinary PWMs for the m left noncensored or observed values. The β^B_r are more complex and use the m observed values and the m-n right-tailed censored values for which the censoring threshold is known. These PWMs are described in the documenation for `pwmRC`.

This function uses the defined relation between to two PWM types when the β^A_r are known along with the parameters (`para`) of a right-tail censored distribution inclusive of the censoring fraction zeta=m/n. The value zeta is the right-tail censor fraction or the probability mathrm{Pr}lbrace rbrace that x is less than the quantile at zeta nonexceedance probability: (mathrm{Pr}lbrace x < X(zeta) rbrace).

β^B_{r-1} = r^{-1}lbracezeta^r r β^A_{r-1} + (1-zeta^r)X(zeta)rbrace mbox{,}

noindent where 1 <= r <= n and n is the number of moments, and X(zeta) is the value of the quantile function at nonexceedance probability zeta. Finally, the `RC` in the function name is to denote `R`ight-tail `C`ensoring.

### Usage

    Apwm2BpwmRC(Apwm,para)

### Arguments

`Apwm` | A vector of A-type PWMs: β^A_r
`para` | The parameters of the distribution from a function such as `pargpaRC` in which the β^A_r are contained in a `list` element titled `betas` and the right-tail censoring fraction zeta is contained in an element titled `zeta`.

### Value

An R `list` is returned.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1995, The use of L-moments in the analysis of censored data, in Recent Advances in Life-Testing and Reliability, edited by N. Balakrishnan, chapter 29, CRC Press, Boca Raton, Fla., pp. 546–560.

### See Also

`Bpwm2ApwmRC` and `pwmRC`

### Examples

    # Data listed in Hosking (1995, table 29.2, p. 551)
    H <- c(3,4,5,6,6,7,8,8,9,9,9,10,10,11,11,11,13,13,13,13,13,
                 17,19,19,25,29,33,42,42,51.9999,52,52,52)
          # 51.9999 was really 52, a real (noncensored) data point.
    z <-  pwmRC(H,52)
    # The B-type PMWs are used for the parameter estimation of the
    # Reverse Gumbel distribution. The parameter estimator requires
    # conversion of the PWMs to L-moments by pwm2lmom().
    para <- parrevgum(pwm2lmom(z$Bbetas),z$zeta) # parameter object
    Bbetas <- Apwm2BpwmRC(z$Abetas,para)
    Abetas <- Bpwm2ApwmRC(Bbetas$betas,para)
    # Assertion that both of the vectors of B-type PWMs should be the same.
    str(Abetas) # A-type PWMs of the distribution
    str(z$Abetas) # A-type PWMs of the original data

[Package lmomco version 0.92 Index]